A model is developed which is capable of predicting the pressure field of a rectangular source, as measured by a finite-sized receiver. This novel method treats the problem in a new way, which allows an integration to be performed over the area of the receiver. Previously it has only been possible to model two circular transducers coaxially aligned. The model is used to identify a receiver, which can be used to measure the highly focussed pressure field from a phased array, with only a negligible effect due to the receiver size. Productions from the model are compared to experimental data, and show a good correlation. A parabolic mirror used to focus the field from a circular device in air has been studied, and a model developed to predict the pressure field produced by this device. This is done by an approximation of the mirror surface to a grid of finely spaced points. The model correlates well with measured results. In addition, an image of a defect in a solid sample was produced. Arrays are then used to image solid samples in air. This is done using three techniques. The first is a combined phased source and receiver, which is shown to locate a wire accurately and to measure a step in the surface of a sample. A 2-D array is shown to image a defect in a composite plate, and the potential for a fast through-transmission air-coupled system is indicated. In addition, two post-processing techniques are used on data recorded using an array receiver, to locate an object in air. Of these two techniques, ellipse crossing is shown to have better results for large signal to noise ratios, and SAFT for lower ratios. The combination of theoretical modelling and experimental observations has indicated that the transducers and arrays constructed for use in air are well-understood, and that their characteristics can be predicted.